From: carlip@physics.ucdavis.edu   
      
   On 4/24/19 3:53 AM, J.B. Wood wrote:   
      
   [...]   
   > Hello, and I wasn't inquiring about the effects of gravity or   
   > whether it's a "true" force or not.  I'm trying to understand its   
   > origin and why it should exist in curved space-time.   
      
   In general, "why" questions aren't really the sort of things physics   
   is good at answering.  In Newtonian physics, for instance, why do   
   objects with no forces acting on them move in straight lines?  You   
   can answer, "Because a straight line is the shortest distance between   
   two point," but why should that matter?  Or you can answer, "Because   
   momentum is conserved," but why should momentum be conserved?  (If   
   you want to be sophisticated, you can say, "Because Noether's theorem   
   implies momentum conservation in a translationally invariant theory   
   derived from an action," but why should the laws of physics be   
   translationally invariant and come from an action?)   
      
   It's helpful to think of general relativity as coming in two parts   
   (more on this below).  First, the presence of matter and energy produces   
   spacetime curvature.  Why?  Well, why should spacetime be flat?  Once   
   you accept that there's no reason beyond prejudice to require flatness,   
   if you're a physicist, you look for an action principle to determine   
   the curvature.  By far the simplest choice (with no extra ingredients   
   like a preferred coordinate system) was discovered by Einstein and   
   Hilbert a century ago, and it leads directly to the Einstein field   
   equations.   
      
   Second, in a curved spacetime, objects move along the shortest possible   
   paths (technically, the *longest* proper time, but that's a technicality   
   coming from the details of the definition).  Why?  Well, it's the   
   obvious generalization of the Newtonian motion along a straight line.   
   It also comes from the simplest action principle you can write down for   
   a point particle.  If you want more than that, I'll again ask the same   
   question in Newtonian physics: why does a free particle move along a   
   straight line?   
      
   Notice that action principles come up in both parts of this answer.   
   Almost all known physics can be written in terms of some version of a   
   principle of least action.  It's likely that this can be traced back to   
   the Feynman path integral in quantum mechanics -- the "paths" in a path   
   integral have phases determined by an action, and the least action   
   configuration is just the stationary phase approximation.  But why   
   should quantum mechanics be described by path integrals?  We don't know.   
      
   Finally, as a slightly more subtle point, the two elements of general   
   relativity I listed aren't really independent.  It turns out that the   
   Einstein field equations -- the equations that determine the curvature   
   of spacetime in terms of its matter content -- are all you need.  If   
   you try to write down a solution of the field equations with two   
   separate lumps of matter, you find that there is no solution for which   
   the lumps are stationary.  Solutions *only* exist if each piece is   
   already moving properly in the other's gravitational field.   
      
   I suspect you won't find this a completely satisfying answer.  But I   
   think that's because you may be asking a wrong question.  Usually when   
   people ask "why" in physics, what they mean is, "Explain this in terms   
   of some phenomenon I already think I understand."  But if you look   
   carefully, you'll find the things you think you already understand are   
   mysterious themselves.  (Balls bouncing off each other? In reality,   
   they never touch; they're repelled by some complex mixture of Pauli's   
   exclusion principle and electromagnetic interactions.)   
      
   Steve Carlip   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)